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arXiv:1208.4914

Solitons and spin transport in an antiferromagnetic spin chain

Nan-Hong Kuo, Sujit Sarkar, Chong Der Hu

Published Aug 24, 2012• 4 citations
arXivHTMLPDF

Abstract

We study the spin transport on a S=1/2 antiferromagnetic chain with external fields which provids a phase angle. The equation of motion becomes the sine-Gordon equation after Jordan-Wigner transformation and bosonization. Soliton solutions of the sine-Gordon equations for a system of finite length are found and the quantum fluctuations are calculated. The spin is transported as the soliton solutions evolves with the adiabatical variation of the phase angle in the phase space. We observe that the spin is transported by ΔS=1, as the phase angle changes by the period of 2π when the quantum fluctuation enables the system makes transition between two solutions. This quantum spin transport is not affected by disturbance of environment.

DOI
10.48550/arxiv.1208.4914

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We study the spin transport on a S=1/2 antiferromagnetic chain with external fields which provids a phase angle. The equation of motion becomes the sine-Gordon equation after Jordan-Wigner transformation and bosonization. Soliton solutions of the sine-Gordon equations for a system of finite length are found and the quantum fluctuations are calculated. The spin is transported as the soliton solutions evolves with the adiabatical variation of the phase angle in the phase space. We observe that the spin is transported by ΔS=1, as the phase angle changes by the period of 2π when the quantum fluctuation enables the system makes transition between two solutions. This quantum spin transport is not affected by disturbance of environment.
We studied the possibility of the spin pump in a S=1/2 antiferromagnetic chain. The spin chain is mapped into a fermion system and bosonization is utilized to transform the equation of motion to a sine-Gordon equation. The sine-Gordon equation on a finite chain with different boundary conditions is solved. Among numerous solutions, the static soliton is compatible with the original physical system. By varying adiabatically a angle in the phase space composed of applied electric and magnetic fields, the spin states change between the Neel state and dimer state and a quantized spin is transported by the bulk state from one end of the system to the other.
We studied the possibility of the spin pump in an S =1/2 antiferromagnetic chain. The spin chain is mapped into a fermion system and bosonization is utilized to transform the equation of motion to a sine-Gordon equation. The solutions of the sine-Gordon equation on a finite chain with different boundary conditions are analyzed. Among numerous solutions, the static soliton is compatible with the original physical system. By varying adiabatically an angle φ in the phase space composed of applied electric and magnetic fields, the spin states change between the Néel state and dimer state and a quantized spin S =1 is transported by the bulk state from one end of the system to the other.
In this paper, we propose the quantum spin pumping in quantum spin systems where an applied electric field (EEE) and magnetic field (HHH) cause a finite spin gap to its critical ground state. When these systems are subject to alternating electromangetic fields; (E,H)=(sin⁡2πtT,cos⁡2πtT)(E,H)=(\sin\frac{2πt}{T},\cos\frac{2πt}{T})(E,H)=(sinT2πt​,cosT2πt​) and travel along the {\it{loop}} ΓloopΓ_{\rm{loop}}Γloop​ which encloses their critical ground state in this EEE-HHH phase diagram, the locking potential in the sine-Gordon model slides and changes its minimum. As a result, the phase operator acquires 2π2π2π holonomy during one cycle along ΓloopΓ_{\rm{loop}}Γloop​, which means that the quantized spin current has been transported through the bulk systems during this adiabatic process. The relevance to real systems such as Cu-benzoate and Yb4As3{\rm{Yb}}_4{\rm{As}}_3Yb4​As3​ is also discussed.
A variational estimate of the free energy of a quantum spin chain based on the stochastic behavior of the quantization axes is proposed. It allows a description of the nonlinear excitations and quantum spin waves within the same framework. For an easy-plane ferromagnet with an external field in the plane it reveals that the nonlinear excitations (solitons) are predominantly described by the classical degrees of freedom. Considerable effort has been devoted to the theoretical description1 and experimental verification of the existence of nonlinear excitations. In this field magnetic chain systems have played an important part.2 Chain systems with an easy-plane anisotropy, such as (C6 H11 NH3 )CuBr3 (CHAB) and CsNiF3 , which are subjected to a symmetry breaking field, were found to be soliton bearing.3 Theoretically the description of the nonlinear effect is based on the mapping of the spin dynamics on a sine-Gordon model. Further research4 indicated that the interpretation of the thermodynamical properties of real systems in terms of the sine-Gordon model required however quantum and anisotropy corrections. Since the dipolar interactions between the spins in the chain are considered to be negligible, the direction of the spin chain in configuration space with respect to any preferred direction in spin space does not enter explicitly in the Hamiltonian. This makes it interesting to define a site-dependent z direction in spin space which makes an angle (Θn ,φn ) with the z direction in configuration space. The model Hamiltonian can then be written in terms of the spin operators defined with respect to the site-dependent quantization axis. The representation with equal quantization axis for all the sites is related to the representation with different quantization axes at each site by a rotation in spin space. The unitary transformation that describes the rotation contains the angles (Θn ,φn ), which we have treated as random variables. Based on this observation we have proposed a new variational approach for the quantum spin chain. We will outline the main results here. A full account is published elsewhere.5 In our approach the free energy of the system can be separated in a quantum part and a classical part. The free energy F of the chain is then approximated by an upper bound F<Fcl +Fqm , where βFcl =−ln[E(exp−βVcl )] and βFqm =−ln Tr(exp−β〈Hqm 〉). The first part is a configurational classical free energy, depending on the choice of the probability distribution for the quantization axes via the expectation E. The second contribution is the free energy of a modified quantum chain, whose parameters are classical averages and can be obtained from the configurational classical free energy. For easy-plane ferromagnetic chains, the nonlinear excitations are comprised in the classical part, whereas the quantum part contains predominantly linear excitations. For those thermodynamical quantities that are insensitive to the contribution of the quantum excitations, the chain is thermodynamically equivalent with a classical sine-Gordon system. The out-of-plane corrections are incorporated in the quantum part of the free energy. This behavior is corroborated experimentally by measurements of the excess heat capacity of CHAB for different magnetic fields with the same in-plane component.6 The validity of our approach is, however, not restricted to easy-plane ferromagnetic chains. Also for more complex systems with, for example, an orthorhombic or helical symmetry, the introduction of stochastic quantization axes can shed new light on some of the thermodynamical properties of these quantum systems in terms of their classical equivalent.
We study spin transport in a one-dimensional finite-length wire connected to fermionic leads. The interacting wire is described by the sine-Gordon model while the leads are either noninteracting or interacting Luttinger liquids. We calculate the spin current driven by a spin bias in the nonlinear regime by solving numerically the classical equation of motion, and find that the cosine term in the sine-Gordon model gives rise to an oscillating spin current when the spin bias exceeds its critical value. We discuss the results in connection with transport experiments with ultracold atoms.